An automaton is complete if for all states q

and all letters a

in the alphabet, there is a transition from q

labeled a

$.$ This may seem strange, given that $\backslash$delta

is a function, so it should always map $($q$,$a$)$

to some state; but in general, $\backslash$delta

is what we call a partial function: there may be pairs mapped to nothing.

However, any incomplete automaton can be made complete by adding one state, usually called a sink state. All missing transitions will point to the sink state, and the sink state will have a self$-$loop on each letter.

In this bonus exercise, you should write the function complete that completes the automaton in place $($that means that you are not allowed to create a new automaton from scratch in that function$).$ You should add a state if and only if the automaton is not complete. Be careful when adding a new state, you should make sure that the state is actually new.

Hint: Have a close look at the documentation, in particular, have a look at the methods inherited. You may also gather some ideas from the testing code.